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Nonlinear Analysis

MA5923Elective Modules9 ECTSEnglishUnregelmäßigDepartment Mathematics
AI-edited module sheet. Based on the TUMonline module description, edited for readability.Original in TUMonline

What it is about

You will learn fundamental methods of nonlinear analysis in infinite dimensions: Schauder degree theory regarding the question whether equations have zeros; generalized versions of inverse and implicit function theorems as well as Lagrange multipliers in the infinite-dimensional context; and bifurcation theory for the study of parameter-dependent solutions and their stability. In the end you will be able to apply these concepts to problems from partial and ordinary differential equations.

What you will be able to do

  • Transfer of essential concepts of finite analysis to infinite dimensions
  • Application of Schauder degree for the existence check of zeros
  • Application of implicit and inverse function theorems in infinite dimensions
  • Understanding of bifurcations, stability, and branching structures of solutions
  • Knowledge of the main ideas of proof methods in these areas

What the module consists of

  • LecturePresentation of the content with examples and discussion to convey the theory
  • ExerciseWorking on concrete examples and problems for deepening and self-check

Teaching method

  • LectureExplanation of the content in lecture form, demonstration through examples and discussion
  • Exercises/Practice SessionsGuided problem solving for deepening and understanding verification
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